riate any stray conclusion she comes
across, without having any _strict_ logical right to it. Assuming _A_,
_B_, _C_, as the ages at first, and _D_ as the number of the years that
have elapsed since then, she finds (rightly) the 3 equations, 2_A_ =
_B_, _C_ = _B_ + _A_, _D_ = 2_B_. She then says "supposing that _A_ = 1,
then _B_ = 2, _C_ = 3, and _D_ = 4. Therefore for _A_, _B_, _C_, _D_,
four numbers are wanted which shall be to each other as 1:2:3:4." It is
in the "therefore" that I detect the unconscientiousness of this bird.
The conclusion _is_ true, but this is only because the equations are
"homogeneous" (_i.e._ having one "unknown" in each term), a fact which I
strongly suspect had not been grasped--I beg pardon, clawed--by her.
Were I to lay this little pitfall, "_A_ + 1 = _B_, _B_ + 1 = _C_;
supposing _A_ = 1, then _B_ = 2 and _C_ = 3. _Therefore_ for _A_, _B_,
_C_, three numbers are wanted which shall be to one another as 1:2:3,"
would you not flutter down into it, oh MAGPIE, as amiably as a Dove?
SIMPLE SUSAN is anything but simple to _me_. After ascertaining that the
3 ages at first are as 3:2:1, she says "then, as two-thirds of their
sum, added to one of them, = 21, the sum cannot exceed 30, and
consequently the highest cannot exceed 15." I suppose her (mental)
argument is something like this:--"two-thirds of sum, + one age, = 21;
[** therefore] sum, + 3 halves of one age, = 31 and a half. But 3 halves of
one age cannot be less than 1 and-a-half (here I perceive that SIMPLE
SUSAN would on no account present a guinea to a new-born baby!) hence
the sum cannot exceed 30." This is ingenious, but her proof, after that,
is (as she candidly admits) "clumsy and roundabout." She finds that
there are 5 possible sets of ages, and eliminates four of them. Suppose
that, instead of 5, there had been 5 million possible sets? Would SIMPLE
SUSAN have courageously ordered in the necessary gallon of ink and ream
of paper?

The solution sent in by C. R. is, like that of SIMPLE SUSAN, partly
tentative, and so does not rise higher than being Clumsily Right.

Among those who have earned the highest honours, ALGERNON BRAY solves
the problem quite correctly, but adds that there is nothing to exclude
the supposition that all the ages were _fractional_. This would make the
number of answers infinite. Let me meekly protest that I _never_
intended my readers to devote the rest of their lives to writing out
answers! E. M. RIX points ou